The table below gives the atomic mass and relative abundance values for the three isotopes of element M.

\begin{tabular}{|c|c|}
\hline
Relative abundance (\%) & Atomic mass (amu) \\
\hline
78.99 & 23.9850 \\
\hline
10.00 & 24.9858 \\
\hline
11.01 & 25.9826 \\
\hline
\end{tabular}

What is the average atomic mass (in amu) of element M?

A. 2.86
B. 5.36
C. 24.30
D. 24.98



Answer :

To determine the average atomic mass of element M, we need to account for both the relative abundances and the atomic masses of its isotopes. Here’s the step-by-step process to calculate the average atomic mass:

1. List the given relative abundances and atomic masses:
- Relative abundance of isotope 1: [tex]\( 78.99\% \)[/tex]
- Atomic mass of isotope 1: [tex]\( 23.9850 \, \text{amu} \)[/tex]
- Relative abundance of isotope 2: [tex]\( 10.00\% \)[/tex]
- Atomic mass of isotope 2: [tex]\( 24.9858 \, \text{amu} \)[/tex]
- Relative abundance of isotope 3: [tex]\( 11.01\% \)[/tex]
- Atomic mass of isotope 3: [tex]\( 25.9826 \, \text{amu} \)[/tex]

2. Convert the relative abundances from percentages to decimal form by dividing by 100:
- Relative abundance of isotope 1: [tex]\( 0.7899 \)[/tex]
- Relative abundance of isotope 2: [tex]\( 0.1000 \)[/tex]
- Relative abundance of isotope 3: [tex]\( 0.1101 \)[/tex]

3. Multiply each isotope's atomic mass by its decimal relative abundance:
- Contribution of isotope 1: [tex]\( 23.9850 \times 0.7899 \)[/tex]
- Contribution of isotope 2: [tex]\( 24.9858 \times 0.1000 \)[/tex]
- Contribution of isotope 3: [tex]\( 25.9826 \times 0.1101 \)[/tex]

4. Sum these contributions:
- Contribution of isotope 1: [tex]\( 23.9850 \times 0.7899 = 18.9482 \, \text{amu} \)[/tex]
- Contribution of isotope 2: [tex]\( 24.9858 \times 0.1000 = 2.4986 \, \text{amu} \)[/tex]
- Contribution of isotope 3: [tex]\( 25.9826 \times 0.1101 = 2.8582 \, \text{amu} \)[/tex]
- Total = [tex]\( 18.9482 + 2.4986 + 2.8582 = 24.3050 \, \text{amu} \)[/tex]

5. Hence, the average atomic mass of element M is:
[tex]\[ 24.3050 \, \text{amu} \][/tex]

Looking at the given choices:
- 2.86
- 5.36
- 24.30
- 24.98

The correct answer is:
[tex]\[ \boxed{24.30} \][/tex]